In one known embodiment such as that described for example in French Patent Specification No. 1,290,867 by the Applicants, the sley joins the upper ends of the two swords, while the oscillating lever mechanisms for controlling two needles, namely: a needle for inserting weft up to the middle of the width of the shed, and a needle for drawing said weft out to the opposite side of the shed, are carried by two casings in the form of boxes fixed respectively on the two ends of the sley and connected with one another by a cap of said sley. Fault may be found with this assembly as not having the full rigidity desirable, especially because it has given thereto an oscillating movement of very high speed which, on modern machines, is inclined to be increased from day to day.